Poincar\'e covariant quantum molecular dynamics: a covariant description of a system of interacting wave packets

TL;DR

This paper introduces a covariant formulation of quantum molecular dynamics that accurately models relativistic interacting wave packets with computational efficiency, applicable to heavy-ion collision simulations.

Contribution

A novel covariant set of equations of motion for quantum molecular dynamics that maintains computational efficiency and improves density-dependent potential estimation.

Findings

Equations of motion are derived from least action principles.

The method accurately estimates density-dependent potentials.

Application to heavy-ion collisions shows robust dynamics approximation.

Abstract

We present a new formulation for the mean-field propagation part of the relativistic quantum molecular dynamics, simulating an $N$-body system of interacting Gaussian wave packets via Lorentz scalar and vector potentials. Covariant equations of motion are derived based on the principle of least action. These covariant equations of motion can be solved with a computational cost comparable to that of conventional noncovariant quantum molecular dynamics. Furthermore, the new equations of motion accurately estimate the density-dependent potential, as demonstrated through comparison of the forces with the numerical integration. We apply them to $N$-body systems interacting via the Skyrme-type potentials or the relativistic mean field to simulate heavy-ion collisions. Our results show that the derived equations of motion provide a robust approximation to the dynamics of the full numerical integrations.